Novel degree function over finite field for LT codes

Abstract

Luby Transform (LT) is a kind of practical Digital Fountain Code. The research on utilizing LT codes over finite field has become more popular. In order to improve the system performance of LT codes over finite field, a novel degree distribution function is proposed in this paper. The main target of this work is trying to improve the decoding success rate with the same overhead (decoding cost) by using a proper degree distribution function, while still keeping the sparse property for the encoding matrix. Numerical simulations are used to show the general performance of our new developed degree distribution function. Various simulation results show that in the environment of LT codes over finite field, using our new degree distribution function, it performs much better than that using the classic degree distribution functions which being used in LT codes and Raptor Code, as the field size increases. This indicates our designed new degree distribution function is suitable to be used in LT codes over finite field in the future.